TN 10th Question Paper 2024 Maths

TN PUBLIC EXAM

QUESTION
PAPER
2024

No. of Printed Pages : 11
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7722
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!7722Mathematics!
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Part - III
Pou® / MATHEMATICS
( uªÌ ©ØÖ® B[Q» ÁÈ / Tamil & English Version)

Põ» AÍÄ : 3.00 ©o ÷|µ® ] [ ö©õzu ©v¨ö£sPÒ : 100
Time Allowed : 3.00 Hours ] [Maximum Marks : 100

AÔÄøµPÒ : (1) AøÚzx ÂÚõUPЮ \›¯õP Aa_¨ £vÁõQ EÒÍuõ GߣuøÚ
\›£õºzxU öPõÒÍÄ®. Aa_¨£vÂÀ SøÓ°¸¨¤ß AøÓU
PsPõo¨£õÍ›h® EhÚi¯õP öu›ÂUPÄ®.
(2) }»® AÀ»x P¸¨¦ ø©°øÚ ©mk÷© GÊxÁuØS®
AiU÷PõikÁuØS® £¯ß£kzu ÷Ásk®. £h[PÒ ÁøµÁuØS
ö£ß]À £¯ß£kzuÄ®.

Instructions : (1) Check the question paper for fairness of printing. If there is any lack of fairness,
inform the Hall Supervisor immediately.
(2) Use Blue or Black ink to write and underline and pencil to draw diagrams.

SÔ¨¦ : CÆÂÚõzuõÒ |õßS £SvPøÍ öPõshx.
Note : This question paper contains four parts.

£Sv & I / PART - I
SÔ¨¦ : (i) AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 14x1=14

(ii) öPõkUP¨£mkÒÍ ©õØÖ ÂøhPÎÀ ªPÄ® Hئøh¯ Âøh°øÚz
÷uº¢öukzxU SÔ±mkhß Âøh°øÚ²® ÷\ºzx GÊuÄ®.
Note : (i) Answer all the questions.
(ii) Choose the most appropriate answer from the given four alternatives and write
the option code and the corresponding answer.

[ v¸¨¦P / Turn over

7722 2

1. n(A×B)=6 ©ØÖ® A={1, 3} GÛÀ, n(B) BÚx :

(A) 1 (B) 2 (C) 3 (-D) 6
If n(A×B)=6 and A={1, 3}, then n(B) is :

(a) 1 (b) 2 (c) 3 (d) 6

2. f : A → B BÚx C¸¦Óa \õº¦ ©ØÖ® n(B)=7 GÛÀ, n(A) BÚx :

(A) 7 (B) 49 (C) 1 (-D) 14
If f : A → B is a bijective function and if n(B)=7, then n(A) is equal to :

(a) 7 (b) 49 (c) 1 (d) 14

3. 1 •uÀ 10 Áøµ²ÒÍ (Cµsk GsPЮ Em£h) AøÚzx GsPÍõ¾® ÁS£k®
ªPa]Ô¯ Gs :
(A) 2025 (B) 5220 (C) 5025 (-D) 2520
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :

(a) 2025 (b) 5220 (c) 5025 (d) 2520

4. J¸ Tmkz öuõhº Á›ø\°À 31 EÖ¨¦PÒ EÒÍÚ. Auß 16 &Áx EÖ¨¦
m GÛÀ, A¢uU Tmkz öuõhº Á›ø\°À EÒÍ GÀ»õ EÖ¨¦PÎß TkuÀ :

31
(A) 16 m (B) 62 m (C) 31 m (-D) 2
m

An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is :

31
(a) 16 m (b) 62 m (c) 31 m (d) m
2

5. x4+64 &I •Ê ÁºUP©õP ©õØÓ ¤ßÁ¸ÁÚÁØÖÒ GøuU Tmh ÷Ásk® ?

(A) 4x 2 (B) 16x 2 (C) 8x 2 (-D) −8x2
Which of the following should be added to make x4+64 a perfect square ?

(a) 4x 2 (b) 16x 2 (c) 8x 2 (d) −8x 2

3 7722

6. J¸ ÷|›¯ \©ß£õmiß Áøµ£h® J¸ __________ BS®.
(A) ÷|ºU÷Põk (B) Ámh® (C) £µÁøͯ® (-D) Av£µÁøͯ®
Graph of a linear equation is a __________.

(a) straight line (b) circle (c) parabola (d) hyperbola

7. ∆ABC &°À DE ?? BC, AB=3.6 ö\.«, AC=2.4 ö\.« ©ØÖ® AD=2.1 ö\.« GÛÀ,
AE &°ß }Í® :

(A) 1.4 ö\.« (B) 1.8 ö\.« (C) 1.2 ö\.« (-D) 1.05 ö\.«
If in ∆ABC, DE ?? BC, AB=3.6 cm, AC=2.4 cm and AD=2.1 cm then the length of AE is :

(a) 1.4 cm (b) 1.8 cm (c) 1.2 cm (d) 1.05 cm

8. Ámhzvß öÁΨ¦Ó¨ ¦Òΰ¼¸¢x ÁmhzvØS GzuøÚ öuõk÷PõkPÒ
Áøµ¯»õ® ?
(A) JßÖ (B) Cµsk
(C) •iÁØÓ GsoUøP (-D) §ä⯮
How many tangents can be drawn to the circle from an exterior point ?

(a) One (b) Two

(c) Infinite (d) Zero

9. (−5, 0), (0, −5) ©ØÖ® (5, 0) BQ¯ ¦ÒÎPÍõÀ Aø©UP¨£k® •U÷Põnzvß
£µ¨¦ :
(A) 0 \. A»SPÒ (B) 25 \. A»SPÒ
(C) 5 \. A»SPÒ (-D) 10 \. A»SPÒ
The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is :

(a) 0 sq. units (b) 25 sq. units

(c) 5 sq. units (d) 10 sq. units

[ v¸¨¦P / Turn over

7722 4

10. x=a tanθ ©ØÖ® y=b secθ GÛÀ,

y2x2 x2y2 x2 y2 x2 y2
(A) 2 2 =1
− (B) 2 − =1 (C) + =1 (D) − =0
b a a b2 a2 b 2 a2 b 2

If x=a tanθ and y=b secθ, then :

y2 x2 x2 y2 x2 y2 x2 y2
(a) − =1 (b) − =1 (c) + =1 (d) − =0
b2 a2 a2 b 2 a2 b 2 a2 b 2

11. 4 ö\.« E¯µ•®, 10 ö\.« Ai¨¦Ó Âmh•® öPõsh J¸ ÷|ºÁmh E¸øÍ°ß
ÁøÍ£µ¨¦ :
(A) 40 π \xµ A»SPÒ (B) 20 π \xµ A»SPÒ
(C) 14 π \xµ A»SPÒ (-D) 80 π \xµ A»SPÒ
The curved surface area of a right circular cylinder of height 4 cm and base diameter 10 cm is :

(a) 40 π sq. units (b) 20 π sq. units

(c) 14 π sq. units (d) 80 π sq. units

12. \©©õÚ Âmh® ©ØÖ® E¯µ® Eøh¯ Kº E¸øÍ, J¸ T®¦ ©ØÖ® J¸
÷PõÍzvß PÚ AÍÄPÎß ÂQu® :
(A) 1 : 2 : 3 (B) 2 : 1 : 3 (C) 1 : 3 : 2 (-D) 3 : 1 : 2
The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter
and same height is :

(a) 1:2:3 (b) 2:1:3 (c) 1:3:2 (d) 3:1:2

13. öPõkUP¨£mh ©v¨¦PÎÀ GøÁ J¸ {PÌa]°ß {PÌuPÁõP C¸UP •i¯õx ?
(A) 0 (B) 0.5 (C) 1.05 (-D) 1
Which of the following values cannot be a probability of an event ?

(a) 0 (b) 0.5 (c) 1.05 (d) 1

5 7722

x
14. J¸ |£¸US ÷Áø» Qøh¨£uØPõÚ {PÌuPÁõÚx 3 . ÷Áø» QøhUPõ©À
2
C¸¨£uØPõÚ {PÌuPÄ 3 GÛÀ, x &Cß ©v¨£õÚx :

(A) 2 (B) 1 (C) 3 (-D) 1.5
x 2
The probability of getting a job for a person is
3
. If the probability of not getting the job is ,
3
then the value of x is :
(a) 2 (b) 1 (c) 3 (d) 1.5

£S-v & II / PART - II
SÔ¨¦ : GøÁ÷¯Ý® 10 ÂÚõUPÐUS Âøh- ¯ - Î U- P - Ä ®. ÂÚõ Gs 28 &US
Pm-hõ-¯-©õP Âøh-¯-ÎU-P-Ä®. 10x2=20

Note : Answer any 10 questions. Question No. 28 is compulsory.

15. A×B={(3, 2), (3, 4), (5, 2), (5, 4)} GÛÀ, A ©ØÖ® B &IU PõsP.

If A×B={(3, 2), (3, 4), (5, 2), (5, 4)} then find A and B.

16. f (x)=3x−2, g(x)=2x+k ©ØÖ® fog=gof GÛÀ, k &Cß ©v¨ø£U PõsP.

If f (x)=3x−2, g(x)=2x+k and fog=gof, then find the value of k.

17. ab×ba=800 GßÓÁõÖ Aø©²® C¸ ªøP •ÊUPÒ ‘a’ ©ØÖ® ‘b’ &IU PõsP.

‘a’ and ‘b’ are two positive integers such that ab×ba=800. Find ‘a’ and ‘b’.

4x 2 y 6 xz 3
18. _¸USP : ×
2z 2 20 y 4

4x 2 y 6 xz 3
Simplify : ×
2z 2 20 y 4

[ v¸¨¦P / Turn over

7722 6

19. ¤ßÁ¸® C¸£ia \©ß£õmiß ‰»[PÎß TkuÀ ©ØÖ® ö£¸UPØ£»ß PõsP.
x 2+8x−65=0

Find the sum and product of the roots for following quadratic equation.

x 2+8x−65=0

20. J¸ ©Ûuß 18 « QÇU÷P ö\ßÖ ¤ßÚº 24 « ÁhU÷P ö\ÀQÓõß. öuõhUP
{ø»°¼¸¢x AÁº C¸US® öuõø»øÁU PõsP.

A man goes 18 m due East and then 24 m due North. Find the distance of his current
position from the starting point.

21. A(−3, 9), B(a, b) ©ØÖ® C(4, −5) Gß£Ú J¸ ÷Põhø©¢u ¦ÒÎPÒ ©ØÖ® a+b=1
GÛÀ, a ©ØÖ® b &°ß ©v¨ø£U PõsP.

If the points A(−3, 9), B(a, b) and C(4, −5) are collinear and if a+b=1, then find a and b.

−5
22. (−1, 2) GßÓ ¦ÒÎ ÁÈ ö\ÀÁx®, \õ´Ä Eøh¯x©õÚ ÷|ºU÷Põmiß
4
\©ß£õmøhU PõsP.

−5
Find the equation of a straight line which has slope and passing through the point
4
(−1, 2).

1 + cosθ
23. = cosecθ + cotθ Gߣøu {¹¤UPÄ®.
1 − cosθ

1 + cosθ
Prove that = cosecθ + cotθ.
1 − cosθ

7 7722

24. J¸ vs© AøµU÷PõÍzvß Ai¨£µ¨¦ 1386 \.« GÛÀ, Auß ö©õzu¨
¦Ó¨£µ¨ø£U PõsP.
If the base area of a hemispherical solid is 1386 sq. metres, then find its total surface area.

25. E¯µ® 2 « ©ØÖ® Ai¨£µ¨¦ 250 \.« öPõsh Kº E¸øÍ°ß PÚ AÍøÁU PõsP.
Find the volume of cylinder whose height is 2 m and base area is 250 sq. m.

26. öPõkUP¨£mh uµÄ¨ ¦ÒÎPÐUS Ãa_ ©ØÖ® Ãa_UöPÊ BQ¯ÁØøÓU PõsP.
25, 67, 48, 53, 18, 39, 44

Find the range and coefficient of range of the following data :

25, 67, 48, 53, 18, 39, 44

27. J¸ ö|mhõsiÀ (leap year) 53 \ÛUQÇø©PÒ Qøh¨£uØPõÚ {PÌuPÄ GßÚ ?
What is the probability that a leap year selected at random will contain 53 Saturdays ?

28. 23 ©ØÖ® 12 BQ¯ÁØÔß «.ö£õ.Á. PõsP.

Find the HCF of 23 and 12.

£S-v & III / PART - III
SÔ¨¦ : GøÁ÷¯Ý® 10 ÂÚõUPÐUS Âøh- ¯ - Î U- P - Ä ®. ÂÚõ Gs 42 &US
Pm-hõ-¯-©õP Âøh-¯-ÎU-P-Ä®. 10x5=50

Note : Answer any 10 questions. Question No. 42 is compulsory.

29. A={x∈N|1<x<4}, ©ØÖ®
B={x∈W|0≤x<2} C={x∈N|x<3} GÛÀ,
A×(B∪C)=(A×B)∪(A×C) Gߣøu \›£õºUPÄ®.

Let A={x∈N|1<x<4}, B={x∈W|0≤x<2} and C={x∈N|x<3}. Then verify that
A×(B∪C)=(A×B)∪(A×C).

[ v¸¨¦P / Turn over

7722 8

30. A={0, 1, 2, 3} ©ØÖ® B={1, 3, 5, 7, 9} Gß£Ú C¸ Pn[PÒ GßP. f : A → B GÝ® \õº¦
f (x)=2x+1 GÚU öPõkUP¨£mkÒÍx. Ca\õº¤øÚU öPõsk

(i) A®¦USÔ £h® (ii) AmhÁøn

(iii) Á›ø\a ÷\õiPÎß Pn® (iv) Áøµ£h®

BQ¯ÁØøÓU SÔUPÄ®

Let A={0, 1, 2, 3} and B={1, 3, 5, 7, 9} be two sets. Let f : A → B be a function given by
f (x)=2x+1. Represent this function

(i) by arrow diagram (ii) in a table form

(iii) as a set of ordered pairs (iv) in a graphical form

31. TkuÀ PõsP : 93+103+.......... 213

Find the sum of 93+103+.......... 213

32. 64x4−16x3+17x2−2x+1 Gߣuß ÁºUP‰»® PõsP.

Find the square root of 64x4−16x3+17x2−2x+1.

 3 1 2
33. A=   GÛÀ, A −5A+7I2=0 GÚ {ÖÄP.
−1 2 

 3 1 2
If A = 
1 2  show that A −5A+7I2=0.
− 

34. ÷uÀì ÷uØÓzøu GÊv {¹¤UPÄ®.

State and prove Thales Theorem.

9 7722

35. (−9, −2), (−8, −4), (2, 2) ©ØÖ® (1, −3) BQ¯ ¦ÒÎPøÍ •øÚPÍõPU öPõsh
|õØPµzvß £µ¨ø£U PõsP.
Find the area of quadrilateral whose vertices are at (−9, −2), (−8, −4), (2, 2) and (1, −3).

36. A(−4, 2) ©ØÖ® B(6, −4) GßÓ ¦ÒÎPøÍ CønUS® ø©¯U SzxU÷Põmiß
\©ß£õmøhU PõsP.
Find the equation of the perpendicular bisector of the line joining the points A(−4, 2) and
B(6, −4).

37. C¸ P¨£ÀPÒ P»[Pøµ ÂÍUPzvß C¸ £UP[Pξ® Ph¼À £¯n®
ö\´QßÓÚ. C¸ P¨£ÀPμ¸¢x P»[Pøµ ÂÍUPzvß Ea]°ß HØÓU
÷Põn[PÒ •øÓ÷¯ 308 ©ØÖ® 458 BS®. P»[Pøµ ÂÍUPzvß E¯µ® 200 «
GÛÀ, C¸ P¨£ÀPÐUS Cøh÷¯ EÒÍ öuõø»øÁU PõsP. ( 3 =1.732)
Two ships are sailing in the sea on either sides of a lighthouse. The angle of elevation of the
top of the lighthouse as observed from the ships are 308 and 458 respectively. If the lighthouse
is 200 m high, find the distance between the two ships. ( 3 =1.732)

38. 45 ö\.« E¯µ•ÒÍ Kº CøhUPshzvß C¸ ¦Ó Bµ[PÒ •øÓ÷¯ 28 ö\.«
©ØÖ® 7 ö\.« GÛÀ, CøhUPshzvß PÚ AÍøÁU PõsP.
If the radii of the circular ends of a frustum which is 45 cm high are 28 cm and 7 cm, find the
volume of the frustum.

39. 6 ö\.« Bµ® ©ØÖ® 15 ö\.« E¯µ® öPõsh J¸ ÷|º Ámh E¸øÍ ÁiÁ¨
£õzvµ® •ÊÁx©õP £ÛUTÌ (Ice-cream) EÒÍx. A¢u¨ £ÛUTÇõÚx, T®¦
©ØÖ® AøµU÷PõÍ® Cøn¢u ÁiÁzvÀ {µ¨£¨£kQÓx. T®¤ß E¯µ® 9 ö\.«
©ØÖ® Bµ® 3 ö\.« GÛÀ, £õzvµzvÀ EÒÍ £ÛUTøÇ {µ¨£ GzuøÚU
T®¦PÒ ÷uøÁ ?
A right circular cylindrical container of base radius 6 cm and height 15 cm is full of
ice-cream. The ice-cream is to be filled in cones of height 9 cm and base radius 3 cm, having
a hemispherical cap. Find the number of cones needed to empty the container.

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7722 10

40. 24, 26, 33, 37, 29, 31 BQ¯ÁØÔß ©õÖ£õmkU öPÊøÁU PõsP.

Find the coefficient of variation of 24, 26, 33, 37, 29, 31.

41. Cµsk £PøhPÒ J¸ •øÓ E¸mh¨£kQßÓÚ. •uÀ £Pøh°À •P ©v¨¦
Cµmøh¨ £øh Gs AÀ»x •P ©v¨¦PÎß TkuÀ 8 &BPU Qøh¨£uØPõÚ
{PÌuPøÁU PõsP.
Two dice are rolled once. Find the probability of getting an even number on the first die or
the total of face sum 8.

42. 7+77+777+.............. GßÓ öuõhº Á›ø\°ß n EÖ¨¦PÎß TkuÀ PõsP.

Find the sum to n terms of the series 7+77+777+..............

£S-v & IV / PART - IV
SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh-¯-ÎU-P-Ä®. 2x8=16

Note : Answer all the questions.

43. (A) PQ=4.5 ö\.«, R = 35 ©ØÖ® Ea] R &°¼¸¢x Áøµ¯¨£mh |kU÷Põmiß
}Í® RG=6 ö\.« GÚ Aø©²©õÖ ∆PQR ÁøµP.
AÀ-»-x
(B) 6 ö\.« Âmh•ÒÍ Ámh® Áøµ¢x Ámhzvß ø©¯zv¼¸¢x 8 ö\.«
öuõø»ÂÀ P GßÓ ¦ÒÎø¯U SÔUPÄ®. A¨¦Òΰ¼¸¢x PA ©ØÖ®
PB GßÓ C¸ öuõk÷PõkPÒ Áøµ¢x AÁØÔß }Í[PøÍ AÍÂkP.

(a) Construct a ∆PQR which the base PQ=4.5 cm, R = 35 and the median RG from R to
PQ is 6 cm.

OR

(b) Draw a circle of diameter 6 cm. from a point P, which is 8 cm. away from its centre.
Draw the two tangents PA and PB to the circle and measure their lengths.

11 7722

44. (A) y=2x2−3x−5 &°ß Áøµ£h® Áøµ¢x, AuøÚ¨ £¯ß£kzv 2x2−4x−6=0
GßÓ \©ß£õmøhz wºUPÄ®.
AÀ-»-x
(B) xy=24, x, y > 0 GßÓ Áøµ£hzøu ÁøµP. Áøµ£hzøu¨ £¯ß£kzv,
(i) x=3 GÛÀ y &IU PõsP.
(ii) y=6 GÛÀ x &IU PõsP.
(a) Draw the graph of y=2x2−3x−5 and hence solve 2x2−4x−6=0.
OR
(b) Draw the graph of xy=24, x, y > 0. Using the graph find,
(i) y when x=3 and
(ii) x when y=6.

-o0o-

[ v¸¨¦P / Turn over

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